Temporal and spatial quantization in nonlinear filtering

One of the most commonly used tools in systems science is that of nonlinear filtering. Applications can be found in control engineering, telecommunications, radar tracking, environmental systems, economics and many other areas. However, despite the wide spread use of these tools, there remain several unresolved issues. The goal of this paper is to give a brief overview of nonlinear filtering. We give particular emphasis to issues related to temporal and spatial quantization.

[1]  Vipin Kumar,et al.  Introduction to Data Mining , 2022, Data Mining and Machine Learning Applications.

[2]  U. Shaked,et al.  H∞ nonlinear filtering , 1996 .

[3]  P. Suchomski,et al.  Numerical conditioning of delta-domain Lyapunov and Riccati equations , 2001 .

[4]  H. Kushner Dynamical equations for optimal nonlinear filtering , 1967 .

[5]  Graham C. Goodwin,et al.  A Novel Technique based on up-sampling for addressing Modeling Issues in Sampled Data Nonlinear Filtering , 2011 .

[6]  Graham C. Goodwin,et al.  Sequential Bayesian Filtering via Minimum Distortion Quantization , 2010 .

[7]  Richard S Bucy LINEAR AND NONLINEAR FILTERING THEORY , 1965 .

[8]  Československá akademie věd,et al.  Transactions of the Fourth Prague Conference on Information Theory, Statistical Decision Functions, Random Processes, held at Prague, from 31st August to 11th September 1965 , 1967 .

[9]  S. P. Lloyd,et al.  Least squares quantization in PCM , 1982, IEEE Trans. Inf. Theory.

[10]  B. Anderson,et al.  Optimal control: linear quadratic methods , 1990 .

[11]  Arnaud Doucet,et al.  A survey of convergence results on particle filtering methods for practitioners , 2002, IEEE Trans. Signal Process..

[12]  A. Jazwinski Stochastic Processes and Filtering Theory , 1970 .

[13]  S. Graf,et al.  Foundations of Quantization for Probability Distributions , 2000 .

[14]  T. Başar,et al.  A New Approach to Linear Filtering and Prediction Problems , 2001 .

[15]  R. Mortensen Stochastic Optimal Control with Noisy Observations , 1966 .

[16]  D. Mayne,et al.  Monte Carlo techniques to estimate the conditional expectation in multi-stage non-linear filtering† , 1969 .

[17]  Graham C. Goodwin,et al.  Variance or spectral density in sampled data filtering? , 2012, J. Glob. Optim..

[18]  T. Kailath,et al.  An innovations approach to least-squares estimation--Part II: Linear smoothing in additive white noise , 1968 .

[19]  W. Wonham Some applications of stochastic difierential equations to optimal nonlinear ltering , 1964 .

[20]  M G Cea,et al.  A discrete nonlinear filter for fast sampled problems based on vector quantization , 2010, Proceedings of the 2010 American Control Conference.

[21]  M. Naumović Sampling in Digital Signal Processing and Control , 2001 .

[22]  Graham C. Goodwin,et al.  Digital control and estimation : a unified approach , 1990 .

[23]  R. L. Stratonovich CONDITIONAL MARKOV PROCESSES , 1960 .

[24]  M. Zakai On the optimal filtering of diffusion processes , 1969 .

[25]  H. Kunita,et al.  Stochastic differential equations for the non linear filtering problem , 1972 .

[26]  Tyrone E. Duncan,et al.  Likelihood Functions for Stochastic Signals in White Noise , 1970, Inf. Control..

[27]  Jeffrey K. Uhlmann,et al.  Unscented filtering and nonlinear estimation , 2004, Proceedings of the IEEE.

[28]  N. Floudas,et al.  A survey of filtering techniques for vehicle tracking by radar equipped automotive platforms , 2005, 2005 7th International Conference on Information Fusion.

[29]  Thomas B. Schön,et al.  Estimation of Nonlinear Dynamic Systems : Theory and Applications , 2006 .

[30]  G. Goodwin,et al.  High-speed digital signal processing and control , 1992, Proc. IEEE.

[31]  Hugh F. Durrant-Whyte,et al.  A new method for the nonlinear transformation of means and covariances in filters and estimators , 2000, IEEE Trans. Autom. Control..

[32]  Tyrone E. Duncan,et al.  On the Absolute Continuity of Measures , 1970 .

[33]  G. Goodwin,et al.  Connection between continuous and discrete Riccati equations with applications to kalman filtering , 1988 .

[34]  Allen Gersho,et al.  Vector quantization and signal compression , 1991, The Kluwer international series in engineering and computer science.